Evolution and formation of dispersive-dissipative patterns

Alexander Oron, Philip Rosenau

Research output: Contribution to journalArticlepeer-review


A variety of interfacial phenomena, including non-Boussinesq and Marangoni effects are described by a dispersive-dissipative model [formula presented]+α[formula presented]+Β[formula presented]+[(1+2u)[formula presented][formula presented]+γ[formula presented]=0. A critical surface α=[formula presented](Β,γ) is found such that for α<[formula presented](Β,γ) the amplitude becomes unbounded within a finite time and the model breaks down. For α>[formula presented](Β,γ), if the initial perturbation is not too large, bounded patterns emerge. The interaction between dispersion and advection dislocates the critical surface (favorably when dispersion and convection cooperate) and suppresses the temporally irregular nature of the resulting patterns. In the first of the two regularized variants of the model considered, the amplitude runaway is mitigated and a formation of cusps is observed. In the second variant with a quadratic dispersion, the emerging solutions are bounded save for a strip in a parameter space, where both the amplitude and the gradients were found to grow at competing rates.

Original languageEnglish
Pages (from-to)R1267-R1270
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number2
StatePublished - 1997


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